[Paper Review] Bilayer two-orbital model of La$_3$Ni$_2$O$_7$ under pressure

Zhihui Luo, Xunwu Hu+3 more|PubMed|May 24, 2023

Iron-based superconductors research50 references35 citations

TL;DR

The authors construct a minimal bilayer two-orbital model for La3Ni2O7 under high pressure (≈29.5–14 GPa regime) based on DFT Wannier downfolding, analyze Fermi-surface topology, and study spin susceptibility within RPA to discuss implications for superconductivity.

ABSTRACT

The newly discovered Ruddlesden-Popper bilayer La_{3}Ni_{2}O_{7} reaches a remarkable superconducting transition temperature T_{c}≈80 K under a pressure of above 14 GPa. Here we propose a minimal bilayer two-orbital model of the high-pressure phase of La_{3}Ni_{2}O_{7}. Our model is constructed with the Ni-3d_{x^{2}-y^{2}}, 3d_{3z^{2}-r^{2}} orbitals by using Wannier downfolding of the density functional theory calculations, which captures the key ingredients of the material, such as band structure and Fermi surface topology. There are two electron pockets, α, β, and one hole pocket, γ, on the Fermi surface, in which the α, β pockets show mixing of two orbitals, while the γ pocket is associated with Ni-d_{3z^{2}-r^{2}} orbital. The random phase approximation spin susceptibility reveals a magnetic enhancement associated with the d_{3z^{2}-r^{2}} state. A higher energy model with O-p orbitals is also provided for further study.

Motivation & Objective

• Motivate and understand the high-pressure superconducting state of La3Ni2O7 by identifying essential low-energy degrees of freedom.
• Provide a minimal bilayer two-orbital tight-binding model that reproduces DFT band structure and Fermi surface near E_F.
• Explore magnetic fluctuations via RPA spin susceptibility to connect orbital content with potential pairing mechanisms.

Proposed method

• Construct a bilayer two-orbital tight-binding model from Wannier downfolding of DFT band structure for the high-pressure phase of La3Ni2O7.
• Define basis Psi_sigma=(d_Ax, d_Az, d_Bx, d_Bz)^T and build H(k)=[[H_A(k), H_AB(k)],[H_AB(k), H_A(k)]] with intra- and inter-layer hoppings as in Eq. (4).
• Include on-site Coulomb interactions with U, U', J and use H_U accordingly.
• Use mirror symmetry to block-diagonalize into bonding/antibonding sectors H_±(k) as in Eq. (12).
• Downfold to an eleven-orbital model to include Ni-d and O-p states and discuss possible Löwdin downfolding for integrating out O-p bands.
• Compute spin susceptibility within RPA using χ_S^(st)(q,iω_n) and Γ as in Eqs. (13)-(19) to identify orbital-resolved magnetic fluctuations.

Experimental results

Research questions

• RQ1 What is the minimal orbital content and bilayer structure needed to capture the high-pressure electronic structure of La3Ni2O7 near E_F?
• RQ2 How does the Fermi-surface topology (α, β electron pockets and γ hole pocket) relate to orbital character and potential pairing channels under pressure?
• RQ3 What is the momentum- and orbital-resolved spin susceptibility in the RPA framework, and which orbitals dominate magnetic fluctuations?
• RQ4 How might interlayer coupling and d_{3z^2−r^2} occupancy influence unconventional superconductivity in this bilayer nickelate?

Key findings

• The DFT-derived band structure under high pressure shows two Ni-d_x2−y2 and Ni-d_3z2−r2 dominated near E_F, with a hole pocket from d_3z2−r2 at the T point and two electron pockets α, β from mixed orbitals.
• A minimal bilayer two-orbital model reproduces the DFT band structure and Fermi surface, yielding a strong interlayer coupling t_bot^z that significantly splits the d_3z2−r2 sector.
• The Fermi surface comprises α, β electron pockets (orbital-mixed) and a γ hole pocket dominated by d_3z2−r2, reflecting the distinct orbital makeup across pockets.
• RPA spin susceptibility shows a ring-like magnetic enhancement with dominant intra-orbital d_3z2−r2 fluctuations, consistent with Fermi-surface nesting of the γ pocket.
• An eleven-orbital model including Ni-d and O-p states is presented, capturing higher-energy physics and suggesting a path for incorporating more complex correlations via DMFT or beyond.
• The study highlights strong interlayer d_3z2−r2 coupling and potential implications for pairing symmetry distinct from cuprates, with suggestions for future exploration of electron-phonon effects under pressure.